Variedades tóricas, fibra de Milnor e equisingularidade de Whitney

Abstract

In this work, we study toric varieties as well as related objects, such as hypersurfaces, along two lines of research. In the first part, we establish conditions on a family of functions defined on an arbitrary toric variety, ensuring that the associated family of hypersurfaces is Whitney equisingular. In the second part, we present a toric structure for the 2-generic symmetric determinantal variety, together with a detailed study of the combinatorics of the cone associated with this structure. As an application, we obtain a formula for computing the Euler characteristic of the Milnor fiber of functions with an isolated singularity at the origin defined on them. Using this formula, we compute the local Euler obstruction of the 2-generic symmetric determinantal variety at the origin. Altogether, the results contribute both to the study of Whitney equisingularity in toric varieties and to the combinatorial and topological understanding of generic symmetric determinantal varieties.